High sensitivity and amenability to miniaturization for field-portable applications have helped to make ion mobility spectrometry (IMS) an important technique for the detection of many compounds, including narcotics, explosives, and chemical warfare agents as described, for example, by G. Eiceman and Z. Karpas in their book entitled “Ion Mobility Spectrometry” (CRC, Boca Raton, 1994). In IMS, gas-phase ion mobilities are determined using a drift tube with a constant electric field. Ions are separated in the drift tube on the basis of differences in their drift velocities. At low electric field strength, for example 200 V/cm, the drift velocity of an ion is proportional to the applied electric field strength, and the mobility, K, which is determined from experimentation, is independent of the applied electric field. Additionally, in IMS the ions travel through a bath gas that is at sufficiently high pressure that the ions rapidly reach constant velocity when driven by the force of an electric field that is constant both in time and location.
E. A. Mason and E. W. McDaniel in their book entitled “Transport Properties of Ions in Gases” (Wiley, New York, 1988) teach that at high electric field strength, for instance fields stronger than approximately 5,000 V/cm, the ion drift velocity is no longer directly proportional to the applied electric field, and K is better represented by KH, a non-constant high field mobility term. The dependence of KH on the applied electric field has been the basis for the development of high field asymmetric waveform ion mobility spectrometry (FAIMS). Ions are separated in FAIMS on the basis of a difference in the mobility of an ion at high field strength, KH, relative to the mobility of the ion at low field strength, K. In other words, the ions are separated due to the compound dependent behavior of KH as a function of the applied electric field strength. It is to be understood that the strength of the field is actually E/N where E is the field in volts/cm and N is the number density of the bath gas. Clearly, the application of lower voltages is appropriate under conditions of lower gas pressure while higher voltages are required at higher gas pressure, each arriving at the same E/N. The behavior of ions in the FAIMS technology is based on changes in the mobility of the ion under conditions of changing E/N, which is often simplified to “conditions of changing electric field strength.”
In general, a device for separating ions according to the FAIMS principle has an analyzer region that is defined by a space between first and second spaced-apart electrodes. By way of example, the first electrode is maintained at a selected dc voltage, often at ground potential, while the second electrode has an asymmetric waveform V(t) applied to it. The asymmetric waveform V(t) is composed of a repeating pattern including a high voltage component, VH, lasting for a short period of time tH and a lower voltage component, VL, of opposite polarity, lasting a longer period of time tL. The waveform is synthesized such that the integrated voltage-time product, and thus the field-time product, applied to the second electrode during each complete cycle of the waveform is zero, for instance VHtH+VLtL=0; for example +2000 V for 10 μs followed by −1000 V for 20 μs. The peak voltage during the shorter, high voltage portion of the waveform is called the “dispersion voltage” or DV, which is identically referred to as the applied asymmetric waveform voltage.
Generally, the ions that are to be separated are entrained in a stream of gas flowing through the FAIMS analyzer region, for example between a pair of horizontally oriented, spaced-apart electrodes. Accordingly, the net motion of an ion within the analyzer region is the sum of a horizontal x-axis component due to the stream of gas and a transverse y-axis component due to the applied electric field. During the high voltage portion of the waveform an ion moves with a y-axis velocity component given by vH=KHEH, where EH is the applied field, and KH is the high field ion mobility under operating electric field, pressure and temperature conditions. The distance traveled by the ion during the high voltage portion of the waveform is given by dH=VHtH=KHEHtH, where tH is the time period of the applied high voltage. During the longer duration, opposite polarity, low voltage portion of the asymmetric waveform, the y-axis velocity component of the ion is vL=KEL, where K is the low field ion mobility under operating pressure and temperature conditions. The distance traveled is dL=vLtL=KELtL. Since the asymmetric waveform ensures that (VHtH)+(VLtL)=0, the field-time products EHtH and ELtL are equal in magnitude. Thus, if KH and K are identical, dH and dL are equal, and the ion is returned to its original position along the y-axis during the negative cycle of the waveform. If at EH the mobility KH>K, the ion experiences a net displacement from its original position relative to the y-axis. For example, if a positive ion travels farther during the positive portion of the waveform, for instance dH>dL, then the ion migrates away from the second electrode and eventually will be neutralized at the first electrode.
In order to reverse the transverse drift of the positive ion in the above example, a constant negative dc voltage is applied to the second electrode. The difference between the dc voltage that is applied to the first electrode and the dc voltage that is applied to the second electrode is called the “compensation voltage” (CV). The CV prevents the ion from migrating toward either the second or the first electrode. If ions derived from two compounds respond differently to the applied high strength electric fields, the ratio of KH to K may be different for each compound. Consequently, the magnitude of the CV that is necessary to prevent the drift of the ion toward either electrode is also different for each compound. Thus, when a mixture including several species of ions, each with a unique KH/K ratio, is being analyzed by FAIMS, only one species of ion is selectively transmitted to a detector for a given combination of CV and DV.
In FAIMS, the optimum dispersion voltage waveform for obtaining the maximum possible ion detection sensitivity takes the shape of an asymmetric square wave with a zero time-averaged value. In practice this asymmetric square waveform is difficult to produce. Since a tuned circuit cannot provide a square wave, an approximation of a square wave is taken as the first terms of a Fourier series expansion. One possible approach is to use:V(t)=A sin(ωt)+B sin(2ωt−Θ)  (1)where V(t) is the asymmetric waveform voltage as a function of time, A is the amplitude of a first sinusoidal wave having frequency ω, B is the amplitude of a second sinusoidal wave having frequency 2ω, and Θ is the phase shift between the first and second sinusoidal waves.
A number of suitable electrode geometries have been described for use with FAIMS. Some examples include electrode geometries that are based on concentric cylinders, parallel flat plates and parallel curved plates. In WO 01/69647, published 20.09.2001, the instant inventor discloses a FAIMS analyzer including four parallel rods arranged as in a conventional linear quadrupole mass spectrometer. A linear quadrupole mass spectrometer employs four parallel spaced hyperbolic surfaces with appropriate voltages to establish a two-dimensional quadrupole field. A popular close approximation to the hyperbolic surfaces uses four parallel spaced round rods. Such mass spectrometers act as a filter, transmitting ions in a selected range of mass-to-charge (m/z) ratios when the ions are injected into one end of the elongated space between the rods.
The quadrupole rods in a linear quadrupole mass spectrometer are used in two ways. If only a radio frequency (rf) sinusoidal waveform is applied to the rods, the rods are said to be operating in rf-only mode. In this mode a wide range of ions of differing mass are transmitted simultaneously. When a vacuum is maintained within the space between the rods, there is a low probability that the ions will collide with a neutral molecule. Alternatively, a bath gas may be present within the space between the rods. Typically, the bath gas pressure is lower than atmospheric pressure, perhaps a few millitorr, which is sufficient to collisionally cool the ions moving through the space between the rods, and to induce collisional dissociation of the ions to form daughter ions or fragment ions. Under these operating conditions, the quadrupole rods define a quadrupole collision cell.
In a second mode, referred to as the mass analyzer mode, a dc voltage is superimposed on the rf sinusoidal waveform voltage that is applied between the rods and the mass range of ions whose trajectories remain stable is significantly reduced. With the appropriate rf and dc voltages, ions within a mass range of one m/z can be stable and all others collide with the walls of the quadrupole rods. Of course, high vacuum conditions are necessary for operation in the mass analyzer mode.
As was mentioned above, a FAIMS mode of operation is also possible by the application of an appropriate combination of asymmetric waveform and dc potentials between the parallel rods. The behavior of ions in the FAIMS technology is based on changes in the mobility of the ion under conditions of changing E/N. The conventional high pressure FAIMS mode of operation is characterized by conditions where the ion reaches constant velocity relatively quickly compared to the time of the application of the field and the distance the ion travels at constant velocity is large compared to the distance traveled before reaching constant velocity. Accordingly, a compromise condition may be envisaged in which the bath gas pressure between the parallel rods is selected to support operation in both the rf-only mode and the FAIMS mode.
The electric field is usually reported as E/N, where E is the field in volts/cm and N is the number density of the gas. For convenience this is reported in Townsend (Td) units, the E/N adjusted by a factor of 1017. For example, at 760 torr the number density is about 2.5×1019, and a field of 12300 volts/cm yield an E/N equivalent to about 50 Td. Note also that at 1 torr a field of 50 Td is about 16 volts/cm. At 50 Td the ion velocity is constant and independent of pressure, assuming that ion mobility varies with pressure as K0(760/P) where K0 is the mobility at 760 torr, and P is the bath gas pressure. This makes the unit of Td convenient to describe mobility changes with electric field strength, i.e. the energetics of collisions between the gas and the ion are independent of pressure at a fixed value of E/N.
Temperature and pressure both affect N, the number density of the gas. Unlike pressure, temperature also affects the mobility of the ion. As described by Mason and McDaniel in their book “Transport properties of Ions in Gases” (Wiley 1988) the temperature has an effect on mobility that is related to the energy of collisions of the ion with the molecules of the bath gas. When the ion is traveling under the influence of an electric field, the effective temperature experienced by the ion deviates from the temperature of the bath gas. This change of mobility caused by change of effective temperature is analogous to the change in mobility that occurs when the bath gas changes temperature. In both cases the ion experiences collisions with higher energy as the temperature increases.
Note also that temperature affects the average velocity of molecules in the gas, and rates of diffusion. The focusing effect in cylindrical FAIMS tends to move the ions to a localized region in space, but the effects of diffusion, space charge ion-ion repulsion and gas turbulence prevent all of the ions from accumulating in small regions, and the ions are actually distributed in space around this ideal focus point. If the effects of diffusion are lower, at lower temperature, the ions may accumulate in a smaller region of space than at higher temperature, where these comparisons are made with equal focusing strengths through virtual or real electric fields. Similarly, a cloud composed of higher density of ions will occupy a larger region in space than a low density cloud, because the electric charges of the ions creates an electric field that may act in opposition to the focusing action of FAIMS and therefore push the ions away from each other.
It is well known that the rf-only quadrupole, and the mass analysis quadrupole, will function well at low pressures (for example 10−7 torr), but will totally fail at pressures above 200 torr. All efforts to use these and other related rf devices at 760 torr have failed.
It is also known that FAIMS will function well at 760 torr, and cannot work at 10−7 torr, where the mean free path between collisions with the gas molecules greatly exceeds the dimensions of the spaces between the electrodes.
In order to function, quadrupoles (and hexapoles, octopoles etc.) require low gas pressures where the ion motion is dominated by momentum. After application of an accelerating force to the ion, the velocity thus acquired remains unchanged in magnitude and direction, unless another force modifies this motion. The motion of an ion in a quadrupole is similar to a marble rolling in a friction free bowl, where the marble may roll quickly along the bottom, and momentum carries it up a side until the kinetic energy is converted to potential energy, or kinetic energy in another direction. This motion is not possible when collisions with the gas remove kinetic energy from the ion, or in the case of the marble rolling in a bowl filled with water where the friction slows the marble until it sits stationary at the bottom of the bowl. These devices work well at low pressures, and gradually deteriorate in function until the gas density causes total failure. This degradation of performance occurs over a range of pressures.
Similarly, FAIMS functions at high pressures, and the function begins to deteriorate at low pressure. At very high pressure, 760 torr for example, the instantaneous application of an electric field causes the ion to accelerate, but in a short time (nanoseconds) the ion reaches a balance where the force from the field exactly matches the magnitude of the ‘friction’ originating from collisions with the gas causing the ion to reach a constant terminal velocity. As the pressure is lowered, and assuming a fixed field of 50 Td (for example), the time required for the ion to reach this terminal velocity is lengthened. If the applied asymmetric waveform is 1 MHz, a delay of less than 10−9 sec for ion acceleration to a constant velocity has minimum consequence to the operation of FAIMS. However, if the ion requires 0.1 μsec or 0.5 μsec to achieve constant velocity, the behavior of the ion no longer is identical to that in the previous example. This is not to say that some component of FAIMS behavior no longer exists, but rather it is now modified.
At its fundamental basis the FAIMS behavior still exists at lower pressures where the only change in the nature of the collisions is a decrease in their frequency of occurrence. Although the concept of ion mobility assumes reaching terminal velocity very quickly, this is not an absolute necessity for the present invention. More important than the time necessary to reach terminal velocity is how this terminal velocity is affected by the field strength. If the waveform exposes the ion to a field of 50 Td for a short time in a first direction and a longer period at 25 Td in an opposite direction, the change in ‘ion mobility’ upon which FAIMS is defined remains functional irregardless of the pressure. If the ion terminal velocity at 760 torr was 5% higher at 50 Td than at 25 Td, this change is present at 100 torr, 10 torr and at 1 torr.
Consider some more details about the conditions at a pressure of 1 torr, and E/N of 50 Td. The applied field at 1 torr is only 16 volts/cm, and the mean free path is 5×10−3 cm. The time to reach terminal velocity is approximately 2 mvd/qE, where m is the mass (kg), vd is expected terminal velocity (m/sec), q is the charge (coul) and E is the field (volts/m). The time to reach terminal velocity is about 0.5 μsec for m/z 200 with K=2 at Standard Temperature and Pressure (STP). The motion of the ion therefore includes a period of acceleration in a first direction, followed by deceleration when the field changed polarity, and acceleration in the second direction followed by deceleration again. The periods of time of acceleration are equal if the final velocity of the ion is based on an ion mobility that is independent of E/N. The period of time of acceleration in high field and low field will differ if the ion mobility is dependent on E/N (the normal situation in FAIMS). This difference in mobility at low and high field translates into two effects: (i) the final terminal velocity, thus distance traveled and (ii) the time required to achieve terminal velocity, also having effect on distance traveled. If the distance traveled during high and low field portions of the waveform are not equal, the equivalent of CV, i.e. a dc offset voltage, will be required to ensure that the ion does not collide with an electrode. The time necessary to achieve terminal velocity is also dependent on the mass of the ion. In other words the CV applied will reflect the m/z of the ion at low pressure. This is because the delay in reaching terminal velocity will require adjustment of CV since the time to reach terminal velocity results in a decrease in the total distance traveled by the ion. This decrease is more significant during the high voltage component of the waveform, which lasts for a shorter time. For example, if the distance traveled during the high voltage period of the waveform would have been 0.1 mm without a period of acceleration, and 0.09 mm because of lost distance during acceleration and 0.1 mm and 0.095 mm respectively during the low voltage period of the waveform, a net drift of the ion will occur. This net drift, as was the case in conventional FAIMS operation, must be compensated for by a dc voltage applied between the electrodes, for the purpose of maintaining ion transmission. The dc voltage will now be a function of both the m/z of the ion and of the change of mobility at high field relative to low field. The recognition of the importance of pressure during the transition from high pressure FAIMS-only mode to low pressure where the momentum of the ion contributes to the motion is critical for understanding the present invention.
In WO 01/69647, the instant inventor disclosed operation of the quadrupole assembly in FAIMS mode when a FAIMS based separation of ions is desired, and operation of the quadrupole assembly in rf-only mode when a FAIMS based separation is not required. In this way, the FAIMS analyzer portion is effectively “electronically removed” from the system when not in use.
Unfortunately, the ions entering the space between the quadrupole assembly, as described in WO 01/69647, may have several electron volts (eV) of translational energy and may be transmitted through the quadrupole assembly in a very short time. Accordingly, the residence time of the ions within the quadrupole assembly may be short and the separation period may be insufficient to achieve an acceptable FAIMS-based separation.
It is an object of the instant invention to provide a method and apparatus that overcomes the limitations of the prior art.